Hemisphere Volume Calculator
Calculate the volume of a hemisphere using radius with our hemisphere volume calculator. Get the hemisphere formula, steps, and instant results.
What Is a Hemisphere?
A hemisphere is exactly one-half of a sphere cut by a plane through its center. It has one curved surface and one flat circular base.
Common examples of hemispheres include domes, bowl-like covers, half-ball molds, and rounded tanks split into two equal parts.
Volume of a Hemisphere Formula
Formula Variables Explained:
The distance from the center of the flat circular face to the outer curved edge of the hemisphere.
The mathematical constant approximately equal to 3.14159265.
A hemisphere has half the volume of a full sphere. Since a sphere volume is V = (4/3) × π × r³, the hemisphere volume becomes V = (2/3) × π × r³.
How to find the volume of a Hemisphere?
- 1Measure the hemisphere radius (r).
- 2Cube the radius: r³ = r × r × r.
- 3Multiply by π.
- 4Multiply the result by 2/3.
- 5Write the final answer in cubic units such as cm³, m³, in³, or ft³.
Example: Calculate the Volume of a Hemisphere
Example 1: Find the volume of a hemisphere with radius 6 cm
Problem: A dome-shaped bowl has a radius of 6 cm. Calculate the volume it can hold.
- Formula: V = (2/3) × π × r³
- Substitute r = 6: V = (2/3) × π × 6³
- Calculate 6³ = 216
- V = (2/3) × π × 216
- V = 144π
- V is approximately 452.39 cm³
Example 2: Calculate hemisphere volume with radius 10 inches
Problem: A half-sphere mold has a radius of 10 inches. Find its enclosed volume.
- Formula: V = (2/3) × π × r³
- Substitute r = 10: V = (2/3) × π × 10³
- Calculate 10³ = 1000
- V = (2/3) × π × 1000
- V is approximately 2094.40 in³
Frequently Asked Questions (FAQ)
Q: Is hemisphere volume exactly half of sphere volume?
Yes. A hemisphere is one-half of a sphere, so its volume is exactly half of the sphere volume formula.
Q: Do I need the diameter to calculate hemisphere volume?
No. Radius alone is enough. If you only know the diameter, divide it by 2 first to get the radius.
Q: What units should the hemisphere volume result use?
Use cubic units that match your input length unit, such as cm³ for centimeters, m³ for meters, or ft³ for feet.